* add support for cold tabulated EOS (P=P(rho)) that

  can be supplemented with a thermal gamma law



git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinEOS/EOS_Omni/trunk@74 8e189c6b-2ab8-4400-aa02-70a9cfce18b9

1 files changed, 72 insertions, 20 deletions

diff --git a/doc/documentation.tex b/doc/documentation.tex
index 743c472..8bbee49 100644
--- a/doc/documentation.tex
+++ b/doc/documentation.tex
@@ -88,7 +88,7 @@ Erik Schnetter \textless eschnetter@perimeterinstitute.ca\textgreater}
 % the date your document was last changed, if your document is in CVS,
 % please use:
 %    \date{$ $Date: 2004-01-07 12:12:39 -0800 (Wed, 07 Jan 2004) $ $}
-\date{April 19, 2011}
+\date{February 24, 2013}
 
 \maketitle
 
@@ -172,6 +172,7 @@ Here,
     \item \texttt{eoskey = 3}: Hybrid EOS (2 Polys, 1 Gamma-Law), used
       for stellar core collapse simulations.
     \item \texttt{eoskey = 4}: Finite-temperature microphysical EOS
+    \item \texttt{eoskey = 5}: Cold tabulated EOS with Gamma-Law
   \end{itemize}
 \item \texttt{havetemp} determines whether the EOS is to be called as
   a function of $(\rho,\epsilon,Y_e)$ (\texttt{havetemp = 0}), or as a
@@ -210,16 +211,9 @@ wrong. This is also true for the Einstein Toolkit GR hydro code
 
 \begin{verbatim}
 eos_omni::poly_gamma 
-eos_omni::poly_gamma_ini 
 eos_omni::poly_k 
 \end{verbatim}
 
-The only non-obvious parameter here is \texttt{poly\_gamma\_ini}.
-In most simulations it should be set equal to \texttt{poly\_gamma}.
-In simulations that are run with a different adiabatic index than
-what was used to set up the initial data, \texttt{poly\_gamma} should
-be the evolution value, and \texttt{poly\_gamma\_ini} should be the initial
-data value.
 
 Check \texttt{param.ccl} for parameters for the other EOS\@.
 
@@ -247,16 +241,7 @@ relation
 \end{eqnarray}
 (which actually ignores the temperature).
 
-Internally, \texttt{EOS\_Omni} uses cgs units, and on startup converts
-the EOS parameters from solar units to cgs units. This conversion
-depends on $\gamma$ and the value of $\gamma$ at the initial
-data stage (\texttt{poly\_gamma\_ini}) is used for this.
-Note that contrary to what the parameter name suggests, 
-\texttt{EOS\_Omni} does not make a distinction between initial data
-setup and time evolution; if such a distinction is required, it must
-be implemented outside of this thorn.
-
-Note also: This polytropic EOS is also used as fall-back when other
+Note: This polytropic EOS is also used as fall-back when other
 EOS fail.
 
 \subsection{Gamma-Law}
@@ -361,7 +346,57 @@ are the following:
 \texttt{nuceos\_table\_name}& STRING & Path/Name of the table file.
 \end{tabular}
 
+\subsection{Cold Tabulated Nuclear EOS with Gamma Law}
+
+Many equations of state for neutron stars are generated under the
+assumption of zero temperature. This is perfectly appropriate for cold
+old neutron stars. In simulations of binary mergers, however, shocks
+will drive the temperature up, adding a thermal pressure component,
+which can be accounted for approximately with a Gamma-Law:
+$P_\mathrm{th} = (\Gamma_\mathrm{th} - 1)\rho\epsilon_\mathrm{th}$\,.
+
+{\tt EOS\_Omni} implements such an equation of state. It reads in an
+ASCII EOS table (see subdirector {\tt tables} for an example table for
+the SLy EOS \cite{douchin:01,haensel:04}, which was generated
+according to the prescription in \cite{shibata:05,corvino:10}). All
+EOS parameters are read from the ASCII file, which has the following
+format:
+
+\begin{verbatim}
+EoSType = Tabulated
+Nrho = 600    NYe = 1     NT = 1
+RhoMin = 1e-09  RhoMax = 0.01
+HeatCapacityE = 1
+GammaTh = 2
+Kappa = 1
+RhoSpacing = Log
+    1.57940636422747e-03    1.38773826035349e+00    2.62139412738900e-02
+[...]
+    2.81804006881059e+00    6.89967555695907e-01    8.30537612378975e-01
+\end{verbatim}
+
+The header completely determines the range in baryon rest mass density
+(in $c=G=M_\odot=1$ units), gives the number of zones (currently only
+{\tt NYe = 1}, {\tt NT = 1}, {\tt HeatCapacityE = 1}, and {\tt
+  RhoSpacing = Log} are supported). {\tt GammaTh} is the
+$\Gamma_\mathrm{th}$ of the thermal gamma law. The tabulated columns
+are $\epsilon$, $\Gamma$, $c_s$ (the speed of sound of the cold
+component of the EOS). The pressure is obtained via $P= \kappa
+\rho^\Gamma$, where $\kappa$ is the {\tt Kappa} scaling parameter.
+
+Generally, $P = P(\rho,\epsilon)$ in this EOS, but note that
+$\epsilon_\mathrm{th} = \epsilon - \epsilon_\mathrm{cold}$. {\tt
+  EOS\_Omni} uses linear interpolation to first find $P(\rho)$ and
+$\epsilon_\mathrm{cold}(\rho)$ and then computes the thermal component
+analytically.
+
 
+\begin{tabular}{lll}
+\texttt{coldeos\_read\_table}& BOOLEAN & Set to {\tt yes} to read table.\\
+\texttt{coldeos\_use\_thermal\_gamma\_law}& BOOLEAN & Set to {\tt yes} to use the thermal
+gamma law (default).\\
+\texttt{coldeos\_table\_name}& STRING & Path/Name of the table file.\\
+\end{tabular}
 
 
 \section{Converting Old Parameter Files}
@@ -386,7 +421,7 @@ this conversion.
   \ref{tab:eosnames}.
 \end{enumerate}
 
-\begin{table}
+\begin{table}[h]
   \begin{tabular}{ll|ll}
     Old Parameter & Old Value & New Parameter & New Value\\
     \hline
@@ -414,7 +449,7 @@ this conversion.
   \label{tab:paramconv}
 \end{table}
 
-\begin{table}
+\begin{table}[h]
   \begin{tabular}{llll}
     EOS    & Description                & Old Name & New Name \\\hline
     poly   & polytropic                 & ???      & 2D\_Polytrope \\
@@ -433,6 +468,23 @@ this conversion.
 
 \bibitem{oconnor:10} O'Connor, E., \& Ott, C.~D.\ 2010, Class. Quantum Grav., 27, 114103 
 
+\bibitem{douchin:01} Douchin, F., \& Haensel, P.\ 2001, Astron.~Astrophys., 380, 151 
+
+\bibitem{haensel:04} Haensel, P., \& Potekhin, A.~Y.\ 2004, Astron.~Astrophys., 428, 191 
+
+\bibitem{shibata:05} Shibata, M., Taniguchi, K., \& Ury{\= u}, K.\ 2005, Phys.~Rev.~D, 71, 084021 
+
+\bibitem{corvino:10} Corvino, G., Rezzolla, L., Bernuzzi, S., De Pietri, R., 
+\& Giacomazzo, B.\ 2010, Class. Quantum Grav., 27, 114104 
+
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